Problem:
Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be ?
Answer Choices:
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Solution:
Let be Pete's present age, and let be Claire's age. Then and . Solving these equations gives and . Thus Pete is years older than Claire, so the ratio of their ages will be when Claire is years old. That will occur years from now.
The problems on this page are the property of the MAA's American Mathematics Competitions